📝 Add and Subtract Decimals in Algebra (21 MCQs)
📖 From Digital SAT Algebra • 1. Basics of Algebra • 21 questions available
What is Add and Subtract Decimals in Algebra?
Definition:
Adding and subtracting decimals in algebra involves combining decimal numbers by aligning decimal points vertically, then adding or subtracting as with whole numbers, ensuring that the decimal point in the result is placed directly below the column of decimal points.
Working:
Write numbers with decimal points aligned; add zeros as placeholders if needed to make equal number of decimal places; add or subtract digits from right to left, carrying or borrowing as necessary; place the decimal point in the answer at the same position.
Example:
Subtract .
Solution: Align: .
Reason:
Decimal addition/subtraction is essential for solving algebraic problems involving money, measurements, and data analysis, and it reinforces place value understanding, which is critical for precise calculations.
📝 All Add and Subtract Decimals in Algebra MCQs
Q1. A shopkeeper records sales of , , and dollars over three transactions, then refunds dollars. What is the final amount kept?
📖 Explanation: First add the three sales: . Then subtract the refund: . The main misconception is forgetting to align decimal places or subtracting the refund before completing the total.
Q2. Two students calculate . Student A writes , while Student B writes . Which reasoning correctly identifies the error?
📖 Explanation: A trailing zero does not change a decimal's value, so equals . Aligning decimal points gives . Student B incorrectly subtracts digits without preserving place value.
Q3. A runner completes three sections of a race measuring km, km, and km. The planned distance is km. How much farther must the runner travel?
📖 Explanation: The completed distance is km. Comparing this with the planned km gives km. Therefore, the runner needs km more. The realistic error is confusing with through poor decimal alignment.
Q4. A number-line display marks , , and . A student claims the distance from to is . What is the correct distance, and why?
📖 Explanation: Distance on a number line is found by subtracting the smaller coordinate from the larger. Writing with aligned decimal places gives . The graph interpretation reinforces that distance measures the interval between two positions.
Q5. A container holds liters of water. First, liters are removed, then liters are added. A student calculates liters. Is the result correct?
📖 Explanation: After removing liters, the container has liters. Adding liters gives liters. The student's arithmetic is incorrect even though the expression setup is appropriate.
Q6. A budget starts at dollars. Three expenses are , , and dollars, while a refund of dollars is received. Which expression correctly models the remaining budget?
📖 Explanation: Expenses reduce the starting budget, so each expense is subtracted. A refund increases the remaining budget, so it is added. Therefore, the correct model is .
Q7. Find two decimals and such that and . Which pair satisfies both conditions?
📖 Explanation: The pair must satisfy both equations simultaneously. Testing and , their sum is and their difference is . This requires coordinating addition and subtraction rather than solving only one condition.
Q8. A student needs to add , , and . Which rewritten form correctly aligns the decimal points before adding?
📖 Explanation: Writing as and as does not change their values. The decimal points are vertically aligned, allowing each digit to occupy the correct place-value column during addition.
Q9. A recipe requires cups of flour, cups of sugar, and cups of another ingredient. A student writes the numbers without adding zeros. What is the best setup?
📖 Explanation: The numbers may have different numbers of decimal digits, but their decimal points must occupy the same vertical position. Trailing zeros are optional, so , , and can be aligned directly without changing their values.
Q10. A student subtracts by placing the directly under the , producing . Which statement best explains the mistake?
📖 Explanation: The in represents tenths, while the in represents hundredths. Aligning the decimal points ensures tenths match tenths and hundredths match hundredths. The incorrect setup changes the place values.
Q11. A number line shows points at , , and . A student says should appear to the right of because . Which conclusion is correct?
📖 Explanation: To compare decimals, corresponding place values must be considered. Writing as makes the comparison clear: . Therefore, appears to the left of on the number line.
Q12. A store receipt lists prices of , , and dollars. The cashier wants to verify the total manually. Which arrangement is most reliable for minimizing place-value errors?
📖 Explanation: The safest arrangement keeps every decimal point in the same column. Although could be written as , it must remain , not . Alignment preserves the original place values and prevents a tenfold error.
Q13. Two methods are proposed for calculating . Method 1 changes to and subtracts . Method 2 changes to and subtracts. Which comparison is correct?
📖 Explanation: Method 1 is valid because , so adding trailing zeros preserves its exact value. Method 2 changes to , which changes the number itself. Therefore, Method 1 preserves the original subtraction.
Q14. Without performing the complete addition, determine the correct setup for . Then identify the place-value issue a careless setup could create.
📖 Explanation: Writing the numbers as , , and creates matching decimal columns without changing their values. A careless setup can shift digits into different place-value columns, producing an answer that may look reasonable but is mathematically incorrect.
Q15. A school purchases supplies costing , , and dollars. A discount of dollars is applied afterward. What is the final cost?
📖 Explanation: First add the three costs: . Then subtract the discount: . Aligning decimal points and preserving place values prevents errors when combining values with different numbers of decimal digits.
Q16. A student claims because they added , then combined the decimal digits . What is the best evaluation of this reasoning?
📖 Explanation: The decimal parts must be aligned by place value. Writing as gives . The student's treats the decimal digits as unrelated whole numbers rather than tenths and hundredths.
Q17. A water tank contains liters. During the morning, liters are used. Later, liters are added. How much water is in the tank afterward?
📖 Explanation: Subtract the amount used first: liters. Then add the amount introduced later: liters. The problem requires interpreting subtraction and addition according to the sequence of real-world changes.
Q18. A number line has points at , , and . What is the total distance traveled when moving from to , then from to ?
📖 Explanation: The first movement is , and the second is . Their sum is . The tempting results from adding the coordinates instead of calculating distances between consecutive points.
Q19. A budget of dollars is changed by three transactions: a payment of , a deposit of , and another payment of . Which expression correctly models the final balance?
📖 Explanation: Payments reduce the balance, while a deposit increases it. Therefore, the correct model subtracts , adds , and subtracts . This produces dollars and demonstrates how decimal operations model sequential financial changes.
Q20. Two students solve . Student A obtains , while Student B obtains . Which result is correct, and what key step supports it?
📖 Explanation: Rewrite as and as . Then , followed by . The error in Student B's work is a hundredths-place addition mistake.
Q21. Find the value of if . Which value satisfies the equation?
📖 Explanation: Combine the known decimal changes: . Therefore, , so . Thus option B is correct. This requires reversing the combined addition and subtraction rather than simply calculating forward.